Applying the 8 Practices During
Hands-on, Collaborative Learning

10story’s tangible, social learning environments are aligned with NCTM’s 8 Effective Mathematical Teaching Practices

Establish mathematics goals to focus learning

Hands-on, collaborative math challenges can help establish clear mathematics goals by providing concrete, engaging activities that naturally highlight the learning objectives. Research suggests that when students understand the purpose of their activities, they are more motivated and better able to see the relevance of the content. Collaborative challenges give students the satisfaction of achieve goals as a group.

Implement tasks that promote reasoning and problem-solving

Research in learning sciences emphasizes the importance of tasks that stimulate higher-order thinking. Hands-on challenges often require students to manipulate physical objects, test hypotheses, and iterate on their solutions, fostering problem-solving skills and reasoning. By working collaboratively, students can share diverse perspectives and strategies, which can lead to deeper understanding and more innovative solutions.

Use and connect mathematical representations

Hands-on activities provide multiple representations of mathematical concepts, from physical models to diagrams and symbols. Students gain a more robust understanding of mathematical ideas when they can see and manipulate different representations. Collaborative work allows students to explain their thinking and see how others approach the same problem, helping them make connections between different forms of representation.

Facilitate meaningful mathematical discourse

Small-group challenges create a natural environment for discourse as students must communicate their ideas, explain their reasoning, and debate solutions. Research indicates that meaningful discourse in math classrooms helps students to clarify their thinking and develop a deeper understanding. Collaborative activities require students to articulate their thoughts and listen to their peers, fostering a culture of mathematical discussion and collective learning.

Pose purposeful questions

Teachers can pose questions to small groups that prompt students to reflect on their actions and decisions during the activity. Educational research shows that purposeful questioning can guide students to deeper understanding and self-discovery. By asking targeted questions, teachers can help students make connections between their hands-on experiences and underlying mathematical concepts.

Build procedural fluency from conceptual understanding

Hands-on challenges often begin with concrete, exploratory activities that lead to abstract conceptual understanding, aligning with research that suggests conceptual understanding should precede procedural fluency. Collaborative work allows students to discuss and refine their strategies, moving from concrete manipulations to more efficient, abstract procedures. This approach helps students see the rationale behind procedures, leading to more robust and flexible mathematical skills.

Support productive struggle in learning mathematics

Struggle, when productive, is essential for learning. When students experience challenges together, they have a safe space to encounter and work through difficulties. Collaborative efforts mean that students can support each other, share strategies, and build resilience together. This collective problem-solving process helps students develop confidence in their mathematical abilities and the ability to persevere.

Elicit and use evidence of student thinking

When students create mathematical artifacts, teachers can observe and gather evidence of their thinking in real-time. Teachers can see how students approach problems, the strategies they use, and their conceptual understanding. This ongoing assessment enables teachers to provide immediate feedback and adjust instruction to better meet students' needs.